Apoptosis induction with taxanes or anthracyclines is the primary therapy for TNBC. Cancer cells can develop resistance to anticancer drugs, causing them to recur and metastasize. Therefore, non-apoptotic cell death inducers could be a potential treatment to circumvent apoptotic drug resistance. In this study, we discovered two novel compounds, TPH104c and TPH104m, which induced non-apoptotic cell death in TNBC cells. These lead compounds were 15- to 30-fold more selective in TNBC cell lines and significantly decreased the proliferation of TNBC cells compared to that of normal mammary epithelial cell lines. TPH104c and TPH104m induced a unique type of non-apoptotic cell death, characterized by the absence of cellular shrinkage and the absence of nuclear fragmentation and apoptotic blebs. Although TPH104c and TPH104m induced the loss of the mitochondrial membrane potential, TPH104c- and TPH104m-induced cell death did not increase the levels of cytochrome c and intracellular reactive oxygen species (ROS) and caspase activation, and cell death was not rescued by incubating cells with the pan-caspase inhibitor, carbobenzoxy-valyl-alanyl-aspartyl-[O-methyl]-fluoromethylketone (Z-VAD-FMK). Furthermore, TPH104c and TPH104m significantly downregulated the expression of the mitochondrial fission protein, DRP1, and their levels determined their cytotoxic efficacy. Overall, TPH104c and TPH104m induced non-apoptotic cell death, and further determination of their cell death mechanisms will aid in the development of new potent and efficacious anticancer drugs to treat TNBC.